Correlation between two fuzzy membership functions

Murthy, C. A.; Pal, Sankar K.; Majumder, D. Dutta

doi:10.1016/0165-0114(85)90004-1

Cited by 97 publications

(30 citation statements)

References 2 publications

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“…It is to be mentioned here that Ihe concept of correlation between twO mcmbership functions as introduced by Murthy and Pal (2) neilher included lhe number of supports in a set nor considered lheir dependenc ies of occurrence. In the present work on image-processing problems.…”

Section: Discussionmentioning

confidence: 99%

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Image segmentation using fuzzy correlation

Pal

Ghosh

1992

Information Sciences

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AOSTKACTA concept or correlation between twO properties (fuzzy repre~cnlations) of an image IS introduced. A sel of algorithms for image segmenLation (both fuvy and nonfuzzy) has been formulated. The spatial infonnation is taken care of by the following measures: transitional correlation and within-class correlation, A relation between the correlation coefficient and thc inde~ of fuzziness is theoretically eSLablished and e~perimenlally verified, The effective ness of the algorithms is illustrated on images having different types of hiSlOgrams.

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Section: Discussionmentioning

confidence: 99%

“…It is to be mentioned here that thL' correlation due to Murthy et a!. [2] considered neither the number of sup[Jort:; of a set, nor the dependencies of their occurrence. Both these factors have bee II taken into account here in implementing this correlation measure on an image…”

Section: Introductionmentioning

confidence: 99%

Image segmentation using fuzzy correlation

Pal

Ghosh

1992

Information Sciences

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“…Note that if product is used instead of min, ROC(A, B) is similar to the Bhattacharyya index for comparing two probability distributions, easily adapted to compare fuzzy sets, namely (Sahnoun et al, 1991) OC Murthy et al (1985) have also adapted the probabilistic notions to the comparison of fuzzy sets, using a standardized squared Euclidean distance, that is the counterpart of a correlation coefficient.…”

Section: Reichenbach Implicationmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

138

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Abstract. This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.

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“…C(Jil' Ji2) between the fuzzy membership functions Jil and Ji2 (defined on the same domain) was defined by Murthy et al (1985), and Pal and Ghosh (1992b Let III (or F J ) denote a fuzzy bright image plane of F having the crossover point at S, say, and be dependent only on grey level. Then Ilz (or F) represents its closest two-tone version thresholded at S. Then the fuzzy correlation between a fuzzy representation of an image and its nearest two-tone version is expressed as…”

Section: Fuzzy Correlationmentioning

confidence: 99%

Segmentation of remotely sensed images with fuzzy thresholding, and quantitative evaluation

Pal

Ghosh

Shankar

2000

International Journal of Remote Sensing

157

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Abstract. Effectiveness of various fuzzy thresholding techniques (based on entropy of fuzzy sets, fuzzy geometrical properties, and fuzzy correlation) is demonstrated on remotely sensed (IRS and SPOT) images. A new quantitative index for image segmentation using the concept of homogeneity within regions is defined. Results are compared with those of probabilistic thresholding, and fuzzy c-means and hard c-means clustering algorithms, both in terms of index value (quantitatively) and structural details (qualitatively). Fuzzy set theoretic algorithms are seen to be superior to their respective non-fuzzy counterparts. Among all the techniques, fuzzy correlation, followed by fuzzy entropy, performed better for extracting the structures. Fuzzy geometry based thresholding algorithms produced a single stable threshold for a wide range of membership variation.

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Correlation between two fuzzy membership functions

Cited by 97 publications

References 2 publications

Image segmentation using fuzzy correlation

Image segmentation using fuzzy correlation

Fuzzy Sets: History and Basic Notions

Segmentation of remotely sensed images with fuzzy thresholding, and quantitative evaluation

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